In the art of flexible hoses or pipes, several attempts have been made to either decrease the diameter of the hose or pipe while keeping the amount of reinforcement equal or to keep the diameter of the hose or pipe constant while increasing the amount of reinforcement. In both cases steel wires or steel cords with higher tensile strengths have been tried. Up to now and in big contrast with rubber tires, however, tests with hoses or pipes having steel cords and steel wires with higher tensile strengths have not been successful. Applying a stress-relieving treatment as disclosed in EP-B1-0 790 349 to the higher tensile steel wires or steel cords, has proved to mitigate the drawbacks of the higher tensile reinforcement in hoses and pipes but, at the same time, has decreased the tensile strength of the steel wires or steel cords.